An open‐top cylindrical can must hold of liquid

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

An open‐top cylindrical can must hold 500 cm3500\text{ cm}^{3} of liquid. The material for the base costs twice as much per square centimeter as the material for the side. Which radius rr (in centimeters) minimizes the total material cost? (a) r≈5.6r\approx5.6 (b) r≈3.4r\approx3.4 (c) r≈4.3r\approx4.3 (d) r≈6.8r\approx6.8

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